Mechanical role of a protein droplet in endocytosis

Max Ferrin

Created: 2021-01-27 Wed 10:24

Acknowledgements

Frank Jülicher The Barnes/Drubin Lab Tyler Harmon

Lab meeting goals

  • Make the model understandable to everyone
  • Get feedback on how to make the story appeal to cell biologists and physical biologists
  • Get feedback on nomenclature

  • Ideas for complementary experiments?

Background/motivation

Mechanical properties of liquid droplets and membranes are generally understood

young_iii_1805
helfrich_elastic_1973

Liquid-like biomolecular condensates are often membrane-associated

banani_biomolecular_2017

Protein droplets and membranes can mechanically influence each other

2D phase separation can induce GUV tubulation autophagosome growth deforms target condensate through wetting
yuan_membrane_2020 agudo-canalejo_wetting_2020

Preliminary evidence for protein phase separation during endocytosis

strong enrichment of likely phase-separating proteins liquid-like network of early proteins required for mammalian endocytosis
tonikian_bayesian_2009 day_liquid-like_2019

Could a protein droplet mechanically assist endocytosis?

Model walk-through

Full model

\begin{equation} F=\sigma\left(S_{o}+S_{m}+S_{i}\right)+\frac{K}{2} S_{i}\left(\frac{2}{R_{i}}-2C_{i}\right)^{2}+\gamma_{d} S_{d}-\gamma_{m} S_{m}-\gamma_{i} S_{i}+P V_{i} \end{equation}
Side view                   Top view

Energy contributions from membrane alone

membrane tension

\(\sigma\left(S_{0}+S_{m}+S_{i}\right)\)

Energy contributions from membrane alone

bending energy

\(\frac{K}{2} S_{i}\left(\frac{2}{R_{i}}-2 C_{i}\right)^{2}\)

Energy contributions from membrane alone

combined membrane tension and bending energy

\(F=\sigma\left(S_{0}+S_{m}+S_{i}\right)+\frac{K}{2} S_{i}\left(\frac{2}{R_{i}}-2 C_{i}\right)^{2}\)

Energy contributions from droplet + membrane

surface tension

\(\gamma_{d} S_{d}\)

Energy contributions from droplet + membrane

wetting energy (note: negative contribution!)

\(\gamma_{m} S_{m}+\gamma_{i} S_{i}\)

Energy contributions from droplet + membrane

combined surface tension and wetting energy

\(F=\gamma_{d} S_{d}-\gamma_{m} S_{m}-\gamma_{i} S_{i}\)

Energy contributions from turgor pressure

\(P V_{i}\)

All contributions together

\(F=\sigma\left(S_{0}+S_{m}+S_{i}\right)+\frac{K}{2} S_{i}\left(\frac{2}{R_{i}}-2 C_{i}\right)^{2}+\gamma_{d} S_{d}-\gamma_{m} S_{m}-\gamma_{i} S_{i}+P V_{i}\)

In progress: parameter sensitivity analysis

Global vs. local invagination stability analysis

boundary diagram                 free energy plot

Increasing droplet volume assists invagination

Increasing droplet volume assists invagination

volume = 107 nm3                 volume = 109 nm3

Increasing droplet volume assists invagination

Increasing droplet volume assists invagination

Increasing wetting energy assists invagination

Increasing wetting energy assists invagination

Increasing wetting energy assists invagination

Future directions

  • Constrain parameters with measured values
  • Compare order of magnitude predictions of unknown parameters to known references
  • Implement more sophisticated membrane geometry model with continuous curvature
  • Any inspiration for experimental design?
  • Devise solution for when droplet is smaller than invagination
  • Think about modeling dynamic processes
    • Droplet size changing over time
    • Bending energy changing over time
    • Forces from actin polymerization
    • Viscoelasticity of the droplet

Thank you!

References

Bibliography

  • [young_iii_1805] Young, III. An Essay on the Cohesion of Fluids, Philosophical Transactions of the Royal Society of London, 95, 65-87 (1805). doi.
  • [helfrich_elastic_1973] Helfrich, Elastic Properties of Lipid Bilayers: Theory and Possible Experiments, Zeitschrift f\"ur Naturforschung C, 28(11-12), 693-703 (1973). doi.
  • [banani_biomolecular_2017] Banani, Lee, Hyman & Rosen, Biomolecular Condensates: Organizers of Cellular Biochemistry, Nature Reviews Molecular Cell Biology, 18(5), 285-298 (2017). doi.
  • [yuan_membrane_2020] Yuan, Alimohamadi, Bakka, Trementozzi, Fawzi, Rangamani & Stachowiak, Membrane Bending by Protein Phase Separation, bioRxiv, 2020.05.21.109751 (2020). doi.
  • [agudo-canalejo_wetting_2020] Agudo-Canalejo, Schultz, Chino, Migliano, Saito, Koyama-Honda, Stenmark, Brech, May, Mizushima & Knorr, Wetting Regulates Autophagy of Phase-Separated Compartments and the Cytosol, Nature, 1-5 (2020). doi.
  • [tonikian_bayesian_2009] Tonikian, Xin, Toret, Gfeller, Landgraf, Panni, Paoluzi, Castagnoli, Currell, Seshagiri, Yu, Winsor, Vidal, Gerstein, Bader, Volkmer, Cesareni, Drubin, Kim, Sidhu & Boone, Bayesian Modeling of the Yeast SH3 Domain Interactome Predicts Spatiotemporal Dynamics of Endocytosis Proteins, PLoS Biology, 7(10), (2009). doi.
  • [li_phase_2012] Li, Banjade, Cheng, Kim, Chen, Guo, Llaguno, Hollingsworth, King, Banani, Russo, Jiang, Nixon & Rosen, Phase Transitions in the Assembly of Multivalent Signalling Proteins, Nature, 483(7389), 336-340 (2012). doi.
  • [day_liquid-like_2019] Day, Kago, Wang, Richter, Hayden, Lafer & Stachowiak, Liquid-like Protein Interactions Catalyze Assembly of Endocytic Vesicles, bioRxiv, 860684 (2019). doi.
  • [lacy_molecular_2018] Lacy, Ma, Ravindra & Berro, Molecular Mechanisms of Force Production in Clathrin-Mediated Endocytosis, FEBS Letters, 592(21), 3586-3605 (2018). doi.